The number that undoes a fraction

2/5 is on the board. What do you multiply it by to get 1?

Turn it upside down

Multiply by 5/2. Then 2/5 × 5/2 = 1.

Swap the two numbers of 2/5 and you get 5/2. Multiply 2/5 by 5/2. On top, 2 × 5 = 10. On the bottom, 5 × 2 = 10. That is 10/10, which is one whole.

The swapped fraction is the reciprocal. Every fraction above zero has one. The pair always multiplies to 1.

• 3/4's reciprocal is 4/3. Check: 3 × 4 = 12 and 4 × 3 = 12.
• A whole number is a fraction over 1. So 6 is 6/1, and its reciprocal is 1/6.

Zero has no reciprocal. Flipping 0/1 gives 1/0. You cannot cut a whole into zero parts.

Slide the top and the bottom in the lab. Make the product exactly 1.

Try the lab to finish this lesson.